6. How is \( \overline{P Q} \) different from \( \stackrel{\rightharpoonup}{P Q} \)

The notation \( \overline{PQ} \) and \( \stackrel{\rightharpoonup}{PQ} \) represent different concepts in geometry and vector mathematics. 1. **\( \overline{PQ} \)**: - This notation typically represents a line segment between points \( P \) and \( Q \). - It indicates that the segment has a definite length and connects the two points directly. - The line segment includes both endpoints \( P \) and \( Q \). 2. **\( \stackrel{\rightharpoonup}{PQ} \)**: - This notation represents a vector from point \( P \) to point \( Q \). - It indicates direction and magnitude but does not include the endpoints as part of the vector itself. - The vector \( \stackrel{\rightharpoonup}{PQ} \) has a specific direction pointing from \( P \) to \( Q \) and can be represented in terms of its components or coordinates. In summary, \( \overline{PQ} \) refers to the physical segment connecting two points, while \( \stackrel{\rightharpoonup}{PQ} \) refers to the directed quantity (vector) that describes the movement from point \( P \) to point \( Q \).